A 25 foot long rectangular sheet of metal, 12 inches wide, is to be made into a rain gutter by turning up two sides so that they are perpendicular to the sheet. How many inches should be turned up to give the gutter its greatest capacity?

The  value is  

Step-by-step explanation:

From the question we are told that

   The  length is  

   The  width is  

Generally let assume that (k ft)  was turned up on each side hence the remaining width is  

Now  the capacity is also the volume it can hold which is mathematically represented as

At maximum  or minimum  

=>    

=>    

Now  to see if the value  obtained is positive or negative we differentiate a second time

    So

at  k  =  0,25 ft

since a negative  value is obtained then k is  the maximum value  

converting to inches

i think there was a typo. you wrote pat brings 3 quarts of ice-cream to the party. each serving of ice-cream is 1 6 quart. how many total servings of ice-cream does pat bring to the party? i think the bold is supposed to be 1/6. so 1 quart of ice cream = 6 servings. 6 * 3 = 18.